What is investment risk as shown in investment products?

Investment risk tells investors by how much the price of an investment deviated from its mean/average in the past.

What is important to know about this investment risk model?

The answers on the risk are inaccurate. The value of this model is it gives to the personal investor an idea what the future could look like not what it will be.

How is investment risk calculated?

It is calculated using the statistical tool of mean and variance (or standard deviation).

Can a personal investor calculate investment risk on his own?

Yes, Microsoft Excel contains the necessary formulas.

The Personal Investor and investment risk or do you know what you are doing? Part 1

Dobromir Risov
3 minutes ago
5 min read

Mag. Dobromir Risov, BSc, September 2026

Surfers.understand and take risk very well. Many personal investors do not understand investment risk.

Introduction

When a surfer rides a wave like the one in the picture above, he needs skills. Those skills are for example knowing the wave, the current and the underground. And assessing if his skills are sufficient to ride the wave safely. Without those skills he risks his health and potentially his life. Gladly for personal investors they don´t risk their health when they make a poor investment decision. However, they lose money. Savings, a personal investor worked for and has given some of their life time in exchange to build up savings. Your investments are important as you are investing portions of your time life. Key for personal investors is understanding investment risk. To use an analogy, the surfer observes the environment before going into the water. Today I cover a widely used concept to describe risk in the capital markets.

Definitions of investment risk found in the internet

What is investment risk? Here are three definitions from different sources:

Investopedia an educational platform writes:

"Risk, in financial terms, is the chance that an outcome or an investment’s actual gains will differ from an expected outcome, usually leaving one worse off."

HSBC a large international bank from the UK writes: :

"Investment risk is simply the probability of incurring losses relative to the expected return on the capital you put into your investments. Different types of investment products carry varying risks,(…)."

The Securities and Exchange Commission of the US writes:

"All investments involve some degree of risk. In finance, risk refers to the degree of uncertainty and/or potential financial loss inherent in an investment decision. In general, as investment risks rise, investors seek higher returns to compensate themselves for taking such risks."

All three sources offer very similar definitions of investment risk. Investment risk is about outcomes, which is a state in the future. They mention expectations, that is an idea about how an investor today imagines the future to be (Forecasting Markets & Stocks). Also, it is mentioned that investors seek higher returns when risk increase. The SEC´s definition mentions the word “uncertainty”. There is a difference between uncertainty and risk: risk can be calculated as the future outcomes are limited. For example when you go into a casino there is no uncertainty. The outcomes are known and so are the probabilities. Risk however is not an exact science, it is an approximation.

Calculate investment risk and understand the answers

I chose the DAX stock market index to show “investment risk”. The DAX is the most important stock market index in Germany, Germany being the third largest economy in the world for 2026. The DAX contains the 40 largest publicly traded companies in Germany. They represent around 80% of the total market capitalisation of publicly traded companies in Germany. Well-known companies like Mercedes or BMW are members of the DAX.

I downloaded the daily values of the DAX for the calender year 2024. I calculated the daily returns using the open prices of each trading day at the stock exchange. Having 253 daily returns I calculated the average return and the standard deviation to describe investment risk.

Table: The results on investment risk at a glimpse.

What are the results? An introduction to mean and standard deviation

In the analysis of the DAX I did, 66% of the daily returns lie in a range of -0,6% and 0,8% or one standard deviation from the mean. The remaining daily returns, or 34% lie outside of that range: those returns lie left from -0,6% and right from 0,8%. The highest daily return, recorded in December 3^rd, is a rare event, to be found on the furthest right side of the distribution. The lowest daily return, a loss of -3%, was recorded on August 2^nd.

On how many days in 2024 did the DAX actually return 0,1%? 17 days. On every other day the daily return was above or below the mean (average) return.

Alternative: How does investment risk change when standard deviation is lower?

Statistically a smaller standard deviation indicates that the majority (66%) of the DAX daily returns lie closer around the average value of 0,1%. In terms of investment risk, that means less risk for the personal investor. These two metrics from the past, mean and standard deviation are used to forecast future investment risk. It is an approximation to forecast future returns. When there is talk about the future, the term expected value instead of average is used.

The investment risk looks bigger, when the scale changes. The figures (table) stay the same. Personal investors keep that in mind. — The investment risk looks bigger, when the scale changes. Keep that in mind.

Application of the data for the personal investor

This risk model tells the personal investor to expect the daily returns of the DAX in 2025 will be between -0,6% and 0,8%. The information offered from these values and this concept is about: “can a personal investor stomach emotionally the daily swings of the capital markets?” Risk is understood in finance academia, as deviation of tomorrow´s stock price from today´s price. It is an important assumption that the stock price equals the value of the stock.

The difference of a statistical (fictional) and actual return for your investments

I showed in the graph above the performance of the DAX and the final amount a personal investor would have at the end of 2024. I show in the table below an alternative: if the DAX went up every trading day by the average calculated, 0,1%. There are no days with less or more return for your investments.

By the end of that year, 1.000€ would accumulate to 1.289€. The Personal investor sees the difference: based on the actual daily returns, 1.000€ accumulated to 1.182€ in 2024. When using the mean daily return instead, it accumulated to 1.289€ by the end of the same period. In the fictional example the personal investor has around 100€ more after one year. This excess profit is for once caused by the lack of losses: when you look at the graph above you see many days where the DAX recorded losses. The example shows the relevance of avoiding losses in successful investing. Yet making losses is part of investing. Some investors freeze at the prospect of making losses and stay by the sidelines. Others are too eager to make big profits and forget about avoiding losses. The path to successful investing is threesome: first knowledge, second its application and third prudence. I discuss individual risk and the role of sampling in part 2.

Frequently Asked Questions (FAQs)

What is investment risk as shown in investment products? Investment risk tells investors by how much the price of an investment deviated from its mean/average in the past.
What is important to know about this investment risk model? The answers on the risk are inaccurate. The value of this model is it gives to the personal investor an idea what the future could look like not what it will be.
How is investment risk calculated? It is calculated using the statistical tool of mean and variance (or standard deviation).
Can a personal investor calculate investment risk on his own? Yes, Microsoft Excel contains the necessary formulas.